692 research outputs found
Regge-Liouville action from group theory
We work out the constraints imposed by SL(2C) invariance for sphere topology
and modular invariance for torus topology, on the discretized form of Liouville
action in Polyakov's non local covariant form. These are sufficient to
completely fix the discretized action except for the overall normalization
constant and a term which in the continuum limit goes over to a topological
invariant. The treatment can be extended to the supersymmetric case.Comment: 4 pages LaTeX, to appear in the proceedings of ``Path Integrals from
peV to TeV'', Florence-Italy, August 25-29, 199
Stationary Solutions in 2+1 Dimensional Gravity and Closed Time-Like Curves
We apply the reduced radial gauge to give the general solution of the metric
in 2+1 dimensions in term of quadratures. It allows a complete controll on the
support of the source. We use the result to prove that for a general stationary
universe, conical at infinity, the weak energy condition and the absence of CTC
at space infinity prevent the occurrrence of any CTC.Comment: Talk presented at Europhysics Conference on High Energy Physics,
Marseille, France, July 22-28 1993, 5 pages, Latex, IFUP-49/9
2+1 Gravity and Closed Time-Like Curves
In this paper we report some results obtained by applying the radial gauge to
2+1 dimensional gravity. The general features of this gauge are reviewed and it
is shown how they allow the general solution of the problem in terms of simple
quadratures. Then we concentrate on the general stationary problem providing
the explicit solving formulas for the metric and the explicit support
conditions for the energy momentum tensor. The chosen gauge allows, due to its
physical nature, to exploit the weak energy condition and in this connection it
is proved that for an open universe conical at space infinity the weak energy
condition and the absence of closed time like curves (CTC) at space infinity
imply the total absence of CTC. It is pointed out how the approach can be used
to examine cosmological solution in 2+1 dimensions.Comment: Talk given at the Workshop on ``Constraint Theory and Quantization
Methods'',10 pages, Latex, IFUP-TH-43/9
The radial gauge propagators in quantum gravity
We give a general procedure for extracting the propagators in gauge theories
in presence of a sharp gauge fixing and we apply it to derive the propagators
in quantum gravity in the radial gauge, both in the first and in the second
order formalism in any space-time dimension. In the three dimensional case such
propagators vanish except for singular collinear contributions, in agreement
with the absence of propagating gravitons.Comment: 38 pages, 1 fig. not available, LATEX, IFUP-TH-30/9
Closed time like curve and the energy condition in 2+1 dimensional gravity
We consider gravity in 2+1 dimensions in presence of extended stationary
sources with rotational symmetry. We prove by direct use of Einstein's
equations that if i) the energy momentum tensor satisfies the weak energy
condition, ii) the universe is open (conical at space infinity), iii) there are
no CTC at space infinity, then there are no CTC at all.Comment: 10 pages (REVTEX 3.0), IFUP-60/9
Polyakov conjecture and 2+1 dimensional gravity coupled to particles
A proof is given of Polyakov conjecture about the auxiliary parameters of the
SU(1,1) Riemann-Hilbert problem for general elliptic singularities. Such a
result is related to the uniformization of the the sphere punctured by n
conical defects. Its relevance to the hamiltonian structure of 2+1 dimensional
gravity in the maximally slicing gauge is stressed.Comment: Talk by P. Menotti at Int. Europhysics Conference on High Energy
Physics, Budapest 12-18 July 2001, 5 pages late
Supersolid phase with cold polar molecules on a triangular lattice
We study a system of heteronuclear molecules on a triangular lattice and
analyze the potential of this system for the experimental realization of a
supersolid phase. The ground state phase diagram contains superfluid, solid and
supersolid phases. At finite temperatures and strong interactions there is an
additional emulsion region, in contrast to similar models with short-range
interactions. We derive the maximal critical temperature and the
corresponding entropy for supersolidity and find feasible
experimental conditions for its realization.Comment: 4 pages, 4 figure
Functional integration on Regge geometries
We adopt the standard definition of diffeomorphism for Regge gravity in D=2 and give an exact expression of the Liouville action in the discretized case. We also give the exact form of the integration measure for the conformal factor. In D>2 we extend the approach to any family of geometries described by a finite number of parameters. The ensuing measure is a geometric invariant and it is also invariant in form under an arbitrary change of parameters
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